It depends on the kind of immigrant. You have students, high educated workforce, people that flee from war/not safe to stay country and people that just want a (economic) better life.
I think too much of any immigration can cause maybe an issue that the majority of people are new and that the culture (how do we interact with each other, what is acceptable behavior etc) has not settled.
So the only way of breaking the cycle is to keep the GOP in power for 8 or 12 years. Result is a massive decline and nobody to blame but themselves. But yeah, that probably won’t work because someone else still gets the blame…